What is your favorite English reference grammar, particularly in terms of accuracy and completeness? Please note: I am not asking for usage guides. What are the strengths and weaknesses of the best ones?
I find Carter and McCarthy's 2006 Cambridge Grammar of English very useful. The great advantage is that it is based on an analysis of real language (the Cambridge International Corpus), which means that its insights are evidence-based, not intuition. Any reference grammars which are not based on corpus evidence are not worth buying.
The book that taught me what little (and how little) I know about English grammar is Huddleston and Pullum's Cambridge Grammar of the English Language. You can read chapter 1 and chapter 2 (PDF) free online. Those are introductory chapters. For a taste of the meat of the book, see this answer regarding the word yesterday, which is basically just a roundup of what CGEL has to say about it.
If you like what you see there, I enthusiastically recommend buying CGEL. It’s unbelievably thorough and accurate. The writing is uniformly clear and concise. Illustrative examples are everywhere. It has both a lexical index (for looking up the peculiar grammar of enough or yesterday) and a conceptual index (for looking up terms like gerund or subject-auxiliary inversion). It's engaging enough to browse as bedtime reading.
The main drawbacks are that it costs $178 and weighs about five pounds.
I used the book Understanding and Using English Grammar by Betty Schrampfer Azar when teaching English throughout the 1990s, mostly for its clear and simplified verb tense diagrams which explain when to use the present progressive, past perfect, present tense, etc.
Please don't mark this as the answer since it is horribly out of date, but just know that H.W. Fowler, The King's English (1908) is a joy to read for its humor, wit, accuracy, and prescriptive adamancy. It is very useful for going into depth of the English language but definitely not a good choice for your first grammar text. Anyone who loves the English language should have a copy of it in their bookcase. You can find it online but do get a paper copy of it, the older and mustier the better.